It seems appropriate to comment on the normalization factor \({\cal N}\) .
In the Bose-Einstein statistics [1]}, we can find the massive photon statistics where
the total number of the photons is countable and fixed so that we can have the constraint of the form \(\sum _{r}n_{r}=N\) . Here
\(n_{r}\)  is the number of photons in quantum state \(r\)  and \(N\)  is the total photon number. However in treating the massless photon
we have a puzzle that, the total number of the massless photons is not fixed so that we cannot have the above constraint on the total number of the photons. Now, this puzzle can be solved by the intrinsic property that the massless photon is a point-like particle without
any size, differently from the massive photon with finite size. After quantization of the light we thus cannot count the number of quantized massless photons. Without resorting to the above constraint on the total number of the photons, the quantum statistics for the massless photon is then known to yield the Planck distribution [1]} \(\bar{n}_{s}=\frac{1}{e^{\beta E_{s}}-1}\) , where \(\beta =1/kT\)  with \(k\)  and \(T\) 
being the Boltzmann constant and temperature, respectively, and \(E_{s}\)  \((s=1,2,...)\)  is the energy in state \(s\) . Next, for the massless
point-like photons, we thus have the normalization factor in (REF ), which is different from that in (REF )
for the massive photon with finite size.
